US5711604A - Method for measuring the coefficient of heat conductivity of a sample - Google Patents
Method for measuring the coefficient of heat conductivity of a sample Download PDFInfo
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- US5711604A US5711604A US08/552,548 US55254895A US5711604A US 5711604 A US5711604 A US 5711604A US 55254895 A US55254895 A US 55254895A US 5711604 A US5711604 A US 5711604A
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- sample
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- 238000000034 method Methods 0.000 title claims abstract description 21
- 239000000523 sample Substances 0.000 claims abstract description 116
- 230000008018 melting Effects 0.000 claims abstract description 22
- 238000002844 melting Methods 0.000 claims abstract description 22
- 238000010438 heat treatment Methods 0.000 claims abstract description 14
- 238000002076 thermal analysis method Methods 0.000 claims abstract description 13
- 239000007787 solid Substances 0.000 claims abstract 21
- 239000004332 silver Substances 0.000 claims description 12
- 230000008859 change Effects 0.000 claims description 9
- 229910052782 aluminium Inorganic materials 0.000 claims description 2
- XAGFODPZIPBFFR-UHFFFAOYSA-N aluminium Chemical compound [Al] XAGFODPZIPBFFR-UHFFFAOYSA-N 0.000 claims description 2
- 229910001220 stainless steel Inorganic materials 0.000 claims description 2
- 239000010935 stainless steel Substances 0.000 claims description 2
- 229910000971 Silver steel Inorganic materials 0.000 claims 1
- 230000009466 transformation Effects 0.000 claims 1
- 239000000463 material Substances 0.000 description 21
- 229910052738 indium Inorganic materials 0.000 description 16
- APFVFJFRJDLVQX-UHFFFAOYSA-N indium atom Chemical compound [In] APFVFJFRJDLVQX-UHFFFAOYSA-N 0.000 description 16
- 238000005259 measurement Methods 0.000 description 12
- BQCADISMDOOEFD-UHFFFAOYSA-N Silver Chemical compound [Ag] BQCADISMDOOEFD-UHFFFAOYSA-N 0.000 description 11
- 229910052709 silver Inorganic materials 0.000 description 11
- 229910052751 metal Inorganic materials 0.000 description 7
- 239000002184 metal Substances 0.000 description 7
- 238000004458 analytical method Methods 0.000 description 6
- 230000004048 modification Effects 0.000 description 6
- 238000012986 modification Methods 0.000 description 6
- 230000004044 response Effects 0.000 description 5
- 239000010409 thin film Substances 0.000 description 5
- 238000001938 differential scanning calorimetry curve Methods 0.000 description 4
- 230000007704 transition Effects 0.000 description 4
- 238000007707 calorimetry Methods 0.000 description 2
- 238000000113 differential scanning calorimetry Methods 0.000 description 2
- 229920003023 plastic Polymers 0.000 description 2
- 239000004033 plastic Substances 0.000 description 2
- 239000002861 polymer material Substances 0.000 description 2
- 230000005855 radiation Effects 0.000 description 2
- 239000011343 solid material Substances 0.000 description 2
- 230000008901 benefit Effects 0.000 description 1
- 238000002425 crystallisation Methods 0.000 description 1
- 230000008025 crystallization Effects 0.000 description 1
- 230000008021 deposition Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 239000011888 foil Substances 0.000 description 1
- 230000004927 fusion Effects 0.000 description 1
- 230000009477 glass transition Effects 0.000 description 1
- 238000000691 measurement method Methods 0.000 description 1
- 238000013208 measuring procedure Methods 0.000 description 1
- 150000002739 metals Chemical class 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
- 238000004154 testing of material Methods 0.000 description 1
- 230000001052 transient effect Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N25/00—Investigating or analyzing materials by the use of thermal means
- G01N25/18—Investigating or analyzing materials by the use of thermal means by investigating thermal conductivity
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N25/00—Investigating or analyzing materials by the use of thermal means
- G01N25/20—Investigating or analyzing materials by the use of thermal means by investigating the development of heat, i.e. calorimetry, e.g. by measuring specific heat, by measuring thermal conductivity
- G01N25/48—Investigating or analyzing materials by the use of thermal means by investigating the development of heat, i.e. calorimetry, e.g. by measuring specific heat, by measuring thermal conductivity on solution, sorption, or a chemical reaction not involving combustion or catalytic oxidation
- G01N25/4846—Investigating or analyzing materials by the use of thermal means by investigating the development of heat, i.e. calorimetry, e.g. by measuring specific heat, by measuring thermal conductivity on solution, sorption, or a chemical reaction not involving combustion or catalytic oxidation for a motionless, e.g. solid sample
- G01N25/4866—Investigating or analyzing materials by the use of thermal means by investigating the development of heat, i.e. calorimetry, e.g. by measuring specific heat, by measuring thermal conductivity on solution, sorption, or a chemical reaction not involving combustion or catalytic oxidation for a motionless, e.g. solid sample by using a differential method
Definitions
- the present invention relates to a method for observing the change in physical characteristics of materials in relation to temperature or time, using a known thermal analyzer.
- the invention relates more particularly to measurement of the coefficient of thermal conductivity of materials using a known differential scanning calorimeter.
- the coefficient of thermal conductivity of a material is an important parameter in material analysis. It is one of the three constants which determine the thermal characteristics of materials, together with thermal diffusibility and specific heat. The following relation exists among those three constants of isotropic materials:
- the third constant can be determined on the basis of the above equation.
- the heat capacity of solid materials can only vary within a range of several orders of magnitude, independent of the type of material.
- the coefficient of thermal conductivity and thermal diffusibility of such materials varies over a range of two to four orders of magnitude as between metals and polymer materials.
- the values of these parameters vary considerably between different polymer materials. Since these differences relate directly to heat radiation characteristics of materials, measurement of the coefficient of thermal conductivity and thermal diffusibility is of great importance, from the industrial point of view, in the field of material testing.
- alternating current heat flow While an alternating current heat flow is supplied to one side of a thin film sample, the frequency or phase of variation of the resulting temperature, detected by a temperature sensor fixed to the sample, is compared with the frequency or phase of alternating current heat flows for obtaining an indication of thermal diffusibility.
- This method is called alternating calorimetry and is disclosed in Japanese Patent Publications Tokkohei 04-79535 and Tokkaihei 03-156351.
- the coefficient of thermal conductivity of the sample can be determined by analyzing the change in temperature at the other side of the sample. This is known as laser flash calorimetry.
- the coefficient of thermal conductivity of the sample can be determined by measuring the temperature differential between the two sides of the sample and comparing the ratio of the magnitude of the heat flow to the temperature differential.
- DSCs are among the most widely used calorimeters and are used for measuring the transition temperatures at a melting point, crystallization point, glass transition point, etc., of sample materials. This subject matter is disclosed in JIS K No. 7121 and JIS H No. 7101. In addition, DSCs are used in fields of physical chemistry analysis such as for measurement of transition heat or radiation heat, or measurement of specific heat, as described in JIS K No. 7123. At the time of calibration of a DSC output temperature, there is employed a procedure which involves difference compensation between the transition temperatures occurring in an empty container and in a container provided with a known sample of a high purity metal having a known transition temperature, under the influence of a constant programming rate of heating.
- the behavior of the resulting DSC curve as the temperature passes through the melting point of the pure metal, with respect to time, is represented by curve 10 in FIG. 2.
- the maximum negative gradient of the curve is proportional to the programming rate of heating and inversely proportional to the thermal resistance between the sample and the heater.
- a temperature calibration method used in existing thermal analyzers is employed and measurement of a high purity sample is made after forming a one-dimensional heat flow path through an unknown sample material and between a temperature sensor and a sample container.
- a sample station of a thermal analyzer for measuring flows of heat into and out of a sample as a function of time or temperature, such as a DSC flows of heat into and out of a sample as a function of time or temperature, such as a DSC, a plate-shaped unknown sample to be measured, having a known thickness and known surface area, and a calibration sample constituted by a high purity metal for temperature calibration are enclosed in a container made of a material having good thermal conductivity and having a bottom area of known size.
- measurements are performed under control of a programmed constant rate of temperature in order to determine the coefficient of thermal conductivity of the unknown sample.
- the peak wave of the DSC curve is analyzed by the above-described measurement in comparison to the curve obtained when the sample is not present.
- the reciprocal of the largest absolute gradient value around the peak of the DSC curve, corresponding to the melting point of the calibration sample, is proportional to the thermal resistance between the calibration sample and the heater. Therefore, by obtaining the difference between the reciprocal of the maximum gradient of the DSC curve with and without the unknown sample present, the incremental value of thermal resistance provided by the measured sample can be determined. Then, by multiplying the programmed rate of temperature by the above-mentioned difference and by the surface area of the container, and then dividing the thickness of the unknown sample material by the product of that multiplication, the value of the coefficient of thermal conductivity of the unknown sample can finally be obtained.
- FIG. 1 is a cross-sectional view of an apparatus employed for performing measurements in accordance with the present invention.
- FIG. 2 is a graph showing thermal analysis curves obtained during the course of measurements according to the invention.
- FIG. 1 shows the basic components of a DSC, including a heat sink 1 made of silver or other material having a good thermal conductivity.
- Sink 1 is made of a material having a good thermal conductivity in order to obtain a homogeneous temperature within the sink.
- a sample holder 3s and a reference holder 3r are mounted within sink 1.
- Holders 3s and 3r are identical to one another and are symmetrically positioned relative to one another in sink 1.
- Holders 3s and 3r are supported in sink 1 by respective elements 2s and 2r having identical thermal resistances.
- Element 2s provides a sample side thermal resistance
- element 2r provides a reference side thermal resistance.
- a temperature sensor 4s and a temperature sensor 4r are mounted at the bottom of sample holder 3s and reference holder 3r, respectively, for measuring the temperatures of sample holder 3s and reference holder 3r.
- Two silver discs 5 are placed on each holder 3r and 3s and a respective sample container 6 is place on each pair of discs 5.
- Each container 6 may be made of a high purity metal having a high coefficient of thermal conductivity, such as aluminum, silver, stainless steel, etc.
- sample 7 On sample holder 3s, a disc-shaped sample 7 to be measured is placed between silver discs 5. Sample 7 has a larger diameter than each disc 5. A high purity indium body 8 is provided in the container 6 which is mounted on sample holder 3s.
- a heater 21 is coiled around the outside of heat sink 1 and is provided for the purpose of heating heat sink 1.
- Heater 21 is connected to a temperature control apparatus 23 for supplying electric power in order to vary the temperature within heat sink 1 according to a predetermined temperature program.
- the operation of temperature control apparatus 23 is controlled in response to the output of a temperature sensor 22 fixed to heat sink 1.
- Temperature sensor 22 supplies a signal representing the temperature of heat sink 1 to apparatus 23.
- DSC apparatus The apparatus shown in FIG. 1 and described above will be referred to hereinafter as DSC apparatus.
- components are disposed in heat sink 1, as illustrated in FIG. 1. Then, in accordance with a selected temperature control program, which may involve a linear increase in the temperature of heat sink 1, heater 21 is operated to effect heating of heat sink 1. During this heating, signals representing the temperatures measured by sensors 4r and 4s are supplied to an operating means 24, where the difference between those temperatures is recorded as a function of time or the temperature measured by sensor 22 or 4r.
- a selected temperature control program which may involve a linear increase in the temperature of heat sink 1
- heater 21 is operated to effect heating of heat sink 1.
- signals representing the temperatures measured by sensors 4r and 4s are supplied to an operating means 24, where the difference between those temperatures is recorded as a function of time or the temperature measured by sensor 22 or 4r.
- Two measuring procedures are performed in the DSC.
- a sample 7 to be measured is provided between the two silver discs 5 on sample holder 3s and temperature apparatus 23 is operated to increase the temperature of sink 1 at a constant rate, the temperature passing through the value at which indium body 8 will melt.
- the differential temperature value applied to operating means 24 varies as a function of time as represented by the solid line curve 10 in FIG. 2.
- the same operation is performed, but with no sample 7 present on holder 3s.
- the resulting variation of the difference in temperature values applied to operating means 24 with respect to time is represented by the broken line curve 11 in FIG. 2.
- operating means 24 calculates the maximum absolute values for the slope of each of curves 10 and 11 at the location associated with the melting point of indium body 8 are calculated, based on the stored data for curves 10 and 11.
- the product of the thickness (t) of sample 7 and the reciprocal of AB is obtained. That product is then multiplied by a term which is equal to the difference between the reciprocals of the maximum gradients of curves 10 and 11 to obtain the value of the coefficient of thermal conductivity of sample 7.
- operating means 24 calculates the largest absolute values for the slopes of curves 10 and 11, which maximum slope values are the slopes of lines 10s and 11s in FIG. 2.
- the DSC output signal which is the difference between the output signal of sensor 4r and the output signal of sensor 4s, is substantially constant with respect to time up to the vicinity of the melting point of indium body 8. This is because both sensor outputs have stable, or linear, temperature characteristics in that temperature range.
- the DSC signal since most of the thermal energy conducted from sink 1 toward body 8 via element 2s is absorbed by indium body 8 as latent heat at the melting temperature of body 8, the DSC signal has a large absolute value. This means that heat flowing to sample holder 3s is absorbed as heat of fusion of indium body 8 so that its temperature does not continue to rise while the temperature of reference holder 4r continues to increase at a constant rate, so that the difference between the temperatures increases.
- Curves 10 and 11 shown in FIG. 2 can be considered to represent the variation of the temperature indicated by sensor 4s minus the temperature indicated by temperature sensor 4r.
- the difference between curves 10 and 11 originates in the difference in heat flow path from the tops of both elements 3s and 3r to the respective sample containers 6, the difference being due to the presence of sample 7 on holder 3s, while a body corresponding to sample 7 is not present on holder 3r.
- the thermal resistance difference between the two paths is equal to the thermal resistance of sample 7.
- the straight lines 10s and 11s represent the tangents to curves 10 and 11 at the location where their slopes have the maximum absolute values.
- the absolute values of the slopes of lines 10s and 11s are P and Q, respectively.
- Q is thus the absolute value of the rate of change of the DSC signal at the melting point of indium when there is no sample 7 present on holder 3s:
- Ro is the thermal resistance from heat sink 1 to indium body 8 when there is no sample 7 on holder 3s.
- P is the absolute value of the rate of change of the DSC signal at the melting point of indium when a sample 7 is present on holder 3s, and particularly between silver discs 5:
- Rs is the thermal resistance from heat sink 1 to indium body 8 when a sample 7 is present on sample holder 3s.
- the thermal resistance R of sample 7 is:
- t is the thickness of sample 7, in the direction between discs 5;
- A is the surface area of the bottom of a silver disc 5, or the surface area of the bottom of sample container 3s when no silver discs are provided, and
- k is the coefficient of thermal conductivity of sample 7.
- the DSC signal may be one which varies with respect to time or temperature, particularly when B is a constant.
- the method according to the invention can be carried out without utilizing silver discs 5, particularly if there is no concern about whether sample 7 will contaminate sample holder 3s when in direct contact therewith, or that the temperature at any point on material 7 will not change due to a lack of contact between material 7 and either the top surface of sample holder 3s or the bottom surface of the associated container 6.
- body 8 can be of a high purity metal other than indium, which has been selected only by way of example, the temperature of indium at which the coefficient of thermal conductivity is determined being in the vicinity of 156° C. For other high purity materials, the measurement may be carried out at a different temperature level.
- DSC apparatus can be utilized for the calculation of the coefficient of thermal conductivity of materials, without any modification of the apparatus. All three constants including thermal diffusibility can also be determined with such DSC apparatus through the combined use of known measurement methods for specific heat and the method according to the invention. Moreover, the coefficient of thermal conductivity of various kinds of solid materials in a form ranging from a thin film to a bulk mass can effectively be determined.
- the thermal analysis curves 10 and 11 which are employed for obtaining values for P and Q can be derived with respect to the temperature of sink 1. Alternatively, they can be determined with respect to time, as shown in FIG. 2, particularly when the temperature control program set by apparatus 23 produces a constant rate of temperature increase.
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- Analytical Chemistry (AREA)
- Biochemistry (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
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- Investigating Or Analyzing Materials Using Thermal Means (AREA)
Abstract
Description
thermal diffusibility×specific heat×density=coefficient of thermal conductivity
Q=B/Ro,
P=B/Rs,
R=t/Ak,
Rs=Ro+R.
Claims (6)
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
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US08/552,548 US5711604A (en) | 1993-12-14 | 1995-11-03 | Method for measuring the coefficient of heat conductivity of a sample |
Applications Claiming Priority (4)
Application Number | Priority Date | Filing Date | Title |
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JP05313671A JP3103963B2 (en) | 1993-12-14 | 1993-12-14 | How to measure thermal conductivity |
JP5-313671 | 1993-12-14 | ||
US35572094A | 1994-12-14 | 1994-12-14 | |
US08/552,548 US5711604A (en) | 1993-12-14 | 1995-11-03 | Method for measuring the coefficient of heat conductivity of a sample |
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US35572094A Continuation-In-Part | 1993-12-14 | 1994-12-14 |
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US5711604A true US5711604A (en) | 1998-01-27 |
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US08/552,548 Expired - Lifetime US5711604A (en) | 1993-12-14 | 1995-11-03 | Method for measuring the coefficient of heat conductivity of a sample |
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US5988875A (en) * | 1997-12-19 | 1999-11-23 | The United States Of America As Respresented By The Department Of Health And Human Services | Calorimeter and method for simultaneous measurement of thermal conductivity and specific heat of fluids |
US6095679A (en) * | 1996-04-22 | 2000-08-01 | Ta Instruments | Method and apparatus for performing localized thermal analysis and sub-surface imaging by scanning thermal microscopy |
US6220748B1 (en) * | 1999-01-15 | 2001-04-24 | Alcoa Inc. | Method and apparatus for testing material utilizing differential temperature measurements |
US20010038660A1 (en) * | 2000-04-26 | 2001-11-08 | Jun Nagasawa | Thermal analysis apparatus |
US6318890B1 (en) * | 1998-10-01 | 2001-11-20 | Mettler-Toledo Gmbh | Single cell calorimeter |
US6331074B1 (en) * | 1997-01-17 | 2001-12-18 | Ricoh Company, Ltd. | Thermal analyzer and a method of measuring with the same |
US6390669B1 (en) * | 1998-07-14 | 2002-05-21 | Seiko Instruments Inc. | Heat flux type differential scanning calorimeter |
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US20020166119A1 (en) * | 2001-05-07 | 2002-11-07 | Cristofalo Michael | System and method for providing targeted programming outside of the home |
US6497509B2 (en) | 2000-06-08 | 2002-12-24 | Perkinelmer Instruments Llc | Method for measuring absolute value of thermal conductivity |
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US6331074B1 (en) * | 1997-01-17 | 2001-12-18 | Ricoh Company, Ltd. | Thermal analyzer and a method of measuring with the same |
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